30 research outputs found
Unrestricted Termination and Non-Termination Arguments for Bit-Vector Programs
Proving program termination is typically done by finding a well-founded
ranking function for the program states. Existing termination provers typically
find ranking functions using either linear algebra or templates. As such they
are often restricted to finding linear ranking functions over mathematical
integers. This class of functions is insufficient for proving termination of
many terminating programs, and furthermore a termination argument for a program
operating on mathematical integers does not always lead to a termination
argument for the same program operating on fixed-width machine integers. We
propose a termination analysis able to generate nonlinear, lexicographic
ranking functions and nonlinear recurrence sets that are correct for
fixed-width machine arithmetic and floating-point arithmetic Our technique is
based on a reduction from program \emph{termination} to second-order
\emph{satisfaction}. We provide formulations for termination and
non-termination in a fragment of second-order logic with restricted
quantification which is decidable over finite domains. The resulted technique
is a sound and complete analysis for the termination of finite-state programs
with fixed-width integers and IEEE floating-point arithmetic
From invasion percolation to flow in rock fracture networks
The main purpose of this work is to simulate two-phase flow in the form of
immiscible displacement through anisotropic, three-dimensional (3D) discrete
fracture networks (DFN). The considered DFNs are artificially generated, based
on a general distribution function or are conditioned on measured data from
deep geological investigations. We introduce several modifications to the
invasion percolation (MIP) to incorporate fracture inclinations, intersection
lines, as well as the hydraulic path length inside the fractures. Additionally
a trapping algorithm is implemented that forbids any advance of the invading
fluid into a region, where the defending fluid is completely encircled by the
invader and has no escape route. We study invasion, saturation, and flow
through artificial fracture networks, with varying anisotropy and size and
finally compare our findings to well studied, conditioned fracture networks.Comment: 18 pages, 10 figure
Statistical investigation of geometrical properties of discontinuities case study: Cavern of rodbar lorestan pumped storage power plant
The geometrical parameters of 639 discontinuities that surveyed in powerhouse cavern of Rodbar Lorestan pumped storage power plant project have been investigated by scanline and areal sampling methods. As regards the processing and correction of bias types, one bedding and three joint sets are existed in the site. The tectonic activities and direction of principal stresses have caused for each of trace length and spacing characteristics, the probability distribution function of joint sets differ to each other as regards their genetic types. The calculated mean trace length by scanline and areal method are very close together for one joint set and for another one the difference is 28%. The actual intensity differences between circular and rectangle sampling windows for joint sets J1 and J2 are 7% and 38%, respectively. Meanwhile, the calculation of volumetric intensity by various methods shows the estimation of this characteristic is very difficult in the field
Strong cut-elimination systems for Hudelmaier’s depth-bounded sequent calculus for implicational logic
Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with proofterms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which gave different arguments for Cut-admissibility suggesting weakly normalising procedures for Cut-elimination, our main reduction system and all its variations are strongly normalising, with the variations corresponding to different optimisations, some of them with good properties such as confluence
Congruence Closure Modulo Associativity and Commutativity
We introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without the need for AC-simplification orderings total on ground terms. Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground AC-theory. This is done by transforming an AC-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction